Answer
$$\lim_{\theta\to0}\frac{\sin(\sin\theta)}{\theta}=1$$
Work Step by Step
$$A=\lim_{\theta\to0}\frac{\sin(\sin\theta)}{\theta}$$ $$A=\lim_{\theta\to0}\frac{\sin(\sin\theta)}{\sin\theta}\times\lim_{\theta\to0}\frac{\sin\theta}{\theta}$$
We have $$\lim_{\theta\to0}\frac{\sin\theta}{\theta}=1$$
For $\lim_{\theta\to0}\frac{\sin(\sin\theta)}{\sin\theta}$, take $\sin\theta=x$, then as $\theta\to0$, we have $x=\sin\theta\to\sin0=0$
So $$\lim_{\theta\to0}\frac{\sin(\sin\theta)}{\sin\theta}=\lim_{x\to0}\frac{\sin x}{x}=1$$
Therefore, $$A=1\times1=1$$
